Math Help - One more area of region bounded by curves question...

1. One more area of region bounded by curves question...

I think I'm getting a good handle on these problems as I do more of them, but this one (I've attached a picture) is tough because it involves trig functions. The intersection points for x are -pi/39 0 and pi/39 so I thought I'd use the integral from -pi/39 to positive pi/39. After integrating and getting -1/13ln(cos(x))-(-2/13)cos(13x) and I keep getting 0. Obviously this isn't right. Where am I going wrong?

2. Originally Posted by fattydq
I think I'm getting a good handle on these problems as I do more of them, but this one (I've attached a picture) is tough because it involves trig functions. The intersection points for x are -pi/39 0 and pi/39 so I thought I'd use the integral from -pi/39 to positive pi/39. After integrating and getting -1/13ln(cos(x))-(-2/13)cos(13x) and I keep getting 0. Obviously this isn't right. Where am I going wrong?
$\int_{-\frac{\pi}{39}}^0 \tan(13x) - 2\sin(13x) \, dx + \int_0^{\frac{\pi}{39}} 2\sin(13x) - \tan(13x) \, dx$

3. Ok...but why?

4. Originally Posted by fattydq
Ok...but why?
look at the graph and see why.